Hi Mickeyz,
Having fixed a lot of phones in my day, I'd say there's a very high probability you need to replace the screen. The issue of whether it's the screen or the cable connecting the screen is moot because the flex cable is integrated into the screen and can't be replaced separately. And since the connector to the motherboard is locked down under a metal cover, it's unlikely that any kind of spontaneous damage could occur without catastrophic damage to the screen itself.
Since this is an older model iPhone, the prices have dropped considerably. The first ones to come up on a search on Amazon were only about $25 USD, which is pretty inexpensive for that repair.
Amazon.com: Black for iPhone 6S Plus 5.5 Inch LCD Screen Replacement Full Digitizer Assembly Frame Set Front Glass 3D Touch Display Required Tool Kit : Cell Phones & Accessories
Of course, if you don't mind paying a bit more and want to support iFixit, you can always purchase the screen here. You can optionally buy it with a "Fix Kit" that has all the tools needed to do the repair.
iPhone 6s Plus Screen: LCD and Digitizer Repair Kit *20% OFF*
Here's the guide to replacing the screen that you'll need. Just follow the instructions from beginning to end and you'll be all set.
iPhone 6s Plus Screen Replacement - iFixit Repair Guide
Good luck with your repair; let us know how it goes!
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